First-principles density functional theoretical study on the structures, reactivity and spectroscopic properties of (NH) and (OH) Tautomer's of 4-(methylsulfanyl)-3[(1Z)-1-(2-phenylhydrazinylidene) ethyl] quinoline-2(1H)-one

The tautomerizations mechanism of 4-(methylsulfanyl)-3[(1Z)-1-(2-phenylhydrazinylidene) ethyl] quinoline-2(1H)-one were inspected in the gas phase and ethanol using density function theory (DFT) M06-2X and B3LYP methods. Thermo-kinetic features of different conversion processes were estimated in temperature range 273–333 K using the Transition state theory (TST) accompanied with one dimensional Eckert tunneling correction (1D-Eck). Acidity and basicity were computed as well, and the computational results were compared against the experimental ones. Additionally, NMR, global descriptors, Fukui functions, NBO charges, and electrostatic potential (ESP) were discussed. From thermodynamics analysis, the keto form of 4-(methylsulfanyl)-3-[(1Z)-1-(2 phenylhydrazinylidene) quinoline-2(1H)-one is the most stable form in the gas phase and ethanol and the barrier heights required for tautomerization process were found to be high in the gas phase and ethanol ~ 38.80 and 37.35 kcal/mol, respectively. DFT methods were used for UV–Vis electronic spectra simulation and the time-dependent density functional theory solvation model (TDDFT-SMD) in acetonitrile compounds.

There is a strong link between structure and stability. Understanding the chemical and physical features of these tautomers could aid future experimental studies on their expected applications, especially their ability to form metal complexes for analytical and biological purposes 15,16 . By comparing the resulting spectra against the experimental data, it is possible to understand the nature of the observed spectra and all its features 17 .

Computational method
Becke's three-parameter and Lee-Yang-Parr hybrid functional (B3LYP) density functional theory (DFT) was used in conjunction with the 6-31G(d,p) basis set [18][19][20] to fully optimize tautomer's and rotamers for their interconversions (detailed structures are given in Supplementary Table S1 in the Supporting information (SI) file). To characterize the nature of each stationary point on the potential energy surface, vibrational mode calculations were performed at the same level of optimization (B3LYP/6-31G(d,p) level). For more accurate energies, the B3LYP/6-31G (d, p) optimized structures were refined at the B3LYP/6-311++G (d, p) and meta-hybrid generalized gradient approximation M06-2X/6-311++G (d, p) levels of theories 21,22 .
where σ, χ(T), k B , T, h, R, P°, and G o (T) refer to the reaction path degeneracy, tunneling correction, Boltzmann constant, temperature in Kelvin, Planck constant, ideal gas constant, the standard pressure and standard Gibbs free energy of activation for reaction, respectively. For unimolecular reactions, Δn = 0.
Tunneling coefficient χ(T) was estimated using the 1D-Eckart tunneling correction (Eck) 33 that previously mentioned in many studies [29][30][31][32] . 1D-Eckart tunneling correction can be obtained numerically by integration of probability of transmission (p(E)) over a Boltzmann distribution of energy as given in Eq. (2): where ΔH f ≠,0K and is the zero-point corrected activation enthalpy in the forward direction. The orbital interactions, atomic charges, and their effects on the structure and stability of the examined structures were calculated using the natural bond orbital (NBO) approach 34 using NBO program version 3.1 35 .
Fukui functions can be extracted from Eqs. (10)(11)(12): where f + (r), f 0 (r), and f -(r) represent nucleophilic, radical, and electrophilic attacks. The dual descriptor ∆f(r) resembles the difference between nucleophilic (Eq. (10)) and electrophilic attacks (Eq. (12)). For different sites, if ∆f(r) > 0, this site tends to undergo a nucleophilic attack. Chemical reactivity towards negative and positive charges could also be expected through mapping electrostatic potential (ESP). For the investigated structures, the electronic absorption spectra (EAS) have been inspected using timedependent density functional theory (TD-DFT) and the Perdew, Burke, and Ernzerhof (PBE) method (abbreviated as TD-PBE) in acetonitrile via the SMD approach at the optimized gas phase geometry of B3LYP/6-31G(d,p), level 46,47 . The accurate PBE0 method can be used to estimate electron excitations for different dye compounds 48,49 . Though, for the inspected molecule compared to experimental results, it gives an underestimation of λ max by 59 nm, whereas TD-PBE functionally overestimates and yields an 11-13 nm difference depending on basis sets. In order to draw the ultraviolet-visible (UV-Vis) spectra, Gauss Sum program 50 was used. For more accurate results, the natural transition orbitals (NTOs) 51 was investigated for different electrons excitations instead of the canonical orbitals. The NTOs were sketched using Gaussview 52 .

Results and discussion
Structural analysis. Previous studies demonstrated the accuracy of M06-2X functional in predicting the stability of tautomers and conformers 21,22,53,54 . Hence, the structures will be considered at B3LYP/6-31G (d, p) and energies at B3LYP/6-31G (d, p), B3LYP/6-311++G (d, p), and M06-2X/6-311++G (d, p). Three isomers of 4-(methylsulfanyl)-3[(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)-one are discussed. Figure 1 shows the optimized structures of different structures at B3LYP/6-31G (d, p) level. To estimate and understand the stability order of the investigated system, reliable structures are necessary. A comparison between theory and experiment must be made to explain the reliability of the obtained data. The B3LYP/6-31G (d, p) level nearly reproduces the structure as obtained from X-ray 17 and this supports the reliability of this level for structure optimization.
Scheme 1 depicts two tautomeric forms of 4-(methylsulfanyl)-3[(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)-one with an intramolecular hydrogen bond (HB). The enol (Quinolinol, E-form) form indicates a phenol-imine HB (O-H···N, 1.816 Å) between the H-atom of the phenolic group and the N atom of the quinoline moiety. It is significant that the short donor-acceptor atom distance in both enol and keto forms provides a suggestion about the presence of a low-barrier hydrogen bond (LBHB), which is between 2.6 and 2.8 Å and has a noted biological importance [55][56][57][58][59][60][61] . The strength of HB in the tautomeric structures can be estimated from the donor (O 15 )-acceptor (N 17 ) distance, which is 1.816 Å in enol form and 2.004 Å in keto form. Accordingly, the enol form has the strongest H-bond. In contrast, rotating the OH hydrogen atom to be far from the acceptor atom (nitrogen atom) gives the corresponding rotamer with no hydrogen bond and increases the donor-acceptor distance to 2.99 Å. Therefore, the keto-enol tautomers will be more stable than the rotamer. Thermodynamics and chemical kinetics. Table 1 collects the barrier height and reaction energy for Keto-Enol reaction in gas phase and ethanol (in parentheses) at the B3LYP/6-31G (d, p) and M06-2X/6-311++G (2d, 2p)//B3LYP/6-31G (d, p) levels, while Fig. 2 shows the potential energy diagram using M06-2X energies.   www.nature.com/scientificreports/ From M06-2X energies, the keto form is the most stable structure followed by rotamer in gas phase and in ethanol. The barrier heights required for the transformation process to the enolare 38.80 and 37.35 kcal/mol, respectively in gas phase and in ethanol, while the transformation of enol to rotamer accompanied barrier heights 12.54 and 11.54 kcal/mol and reaction energies 2.10 and 2.13 kcal/mol in gas phase and ethanol, respectively relative to keto form. The intrinsic reaction coordinates (IRC) and the potential energy changes during keto-enol conversion were drawn in Supplementary Figs. S1 and S2 (SI), respectively. From Supplementary Fig. S1, O-H bond is formed gradually with the breaking of the N-H bond and the two curves cross each other at s = 0 amu 1/2 bohr. The formed N-C bond and the broken C-O bond are gently formed during the progress of the reaction. The calculated rate coefficients for the selected transitions at TST and 1D-Eck tunneling are given in Table 2. The results show that, the rate of the transformation of keto to enol in ethanol is higher about 12-20 times than in gas phase and a high effect for tunneling correction during the applied range of temperature especially for Keto-enol reaction compared to the enol-rotomar conversion.

NMR analysis.
In the NMR spectrum, the development of a low-field proton signal (high chemical shifts) is a well-known effect of forming a hydrogen bond with a sign for an LBHB [62][63][64] . Table 3 contains the complete data on NMR in enol, keto, and rotamer at B3LYP/6-31G(d,p) in comparison to experimental NMR. Figure 3 shows the calculated 13 C and 1 H NMR chemical shifts for 4-(methylsulfanyl)-3[(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)-one in CHCl 3 agree well with the experimental results 8 . Table 3 shows that C 18 in the  DFT reactivity descriptors and Fukui function. Table 2 shows the energies of LUMO, HOMO, the energy gap (E g ), vertical IP, EA, η,S, χ, µ and ω . The IP represents the ability to donate an electron, while the EA illustrates the ability to accept an electron. According to Table 4, the keto form has the smallest HOMO-LUMO gap (3.00 eV), followed by rotamer (3.53 eV). The enol form has the highest gap (3.78 eV). The smaller the energy gaps, the higher the reactivity of the molecule 66,67 . So, the keto form is expected to have high chemical reactivity, low hardness, and high softness compared to enol and their rotamers. The keto form can act as an electron donor and acceptor by having the highest HOMO energy (E HOMO = − 5.36 eV, the lowest value of the IP) and the lowest LUMO energy (E LUMO = − 2.36 eV, the largest value of the affinity). However, based on the calculations, ω and η they are better suited to act as strong electrophiles. A good electrophile has a high chemical www.nature.com/scientificreports/ potential as well as a low hardness 68 . Because the keto form has the highest electronegativity (χ = 3.86 eV) and the most negative chemical potential, it is the best electron acceptor.
To determine the most favorable place to add or remove an electron from a molecule, one looks at the chemical reactivity, which is one of the most fundamental questions. Electron density distributions are basic to understanding electrophilic and nucleophilic attacks. Table 5 shows the calculated condensed Fukui function value for enol and keto forms, and values for rotamers are given in the supporting information.
From Table 5 values, the electrophilic attack order for enol in the gas phase is C6 > N17 > C4 > C5 > C9 > C1 4 > C13 > C12. The C6 and N17 atoms have a higher fvalue, indicating possible electron acceptor sites. There is some evidence that reactive electrophilic sites are primarily found on the hydrazinylidene ring. Conversely, for the nucleophilic attack, the reactivity order is C6 > C4 > C14 > C33 > C34. According to the dual descriptor (∆f) > 0 value for N17 and O15, these sites are favored for nucleophilic attack. As well as all hydrogen atoms, H is highly nucleophilic and H7 is highly electrophilic.
The C6, C4, C14, C12, N29, C5, C13, and C9 atoms in keto form are more sensitive sites for accepting electrons, and the C6, C14, C9, C5, C12, C13, C20, and C4 atoms are the most favorable sites for electron donation. Hence, heterocyclic rings are the most reactive sites for electron donor-acceptor interactions. The C20 and N29 atoms have a very positive dual descriptor (∆f) value, indicating a proclivity to donate electrons. According to the highly negativity dual descriptor (∆f), the C20 and C4 atoms are the most favorable sites for accepting electrons. Because it has the highest values of f − and f + in both enol and keto forms, the C6 atom is a suitable site for both electrophilic and nucleophilic attacks.
For rotamer form, it is observed that C9, C5, C12, C13, C14, and C6 atoms have a higher fvalue, which shows the possible site for electrophilic attack, and C6, C12, C4, C13, and C14 have a higher f + value which indicates the possible site for nucleophilic attack. The dual descriptor (∆f) values of C12, C13, and C6 are highly positive; they have the tendency to donate electrons. On the contrary, N17 and O15 are susceptible to acquiring electrons.
Charge distribution and ESP analysis. The electrostatic potential (ESP) and charge distribution surface are broadly used to determine the reactivity of a given molecule and its expected interaction with other systems. The NBO charges of the investigated structures have been calculated in Table 6 in the gas phase at the B3LYP/6-31G (d, p) level. In agreement with the Fukui function results, the NBO charges calculations for 4-(methylsulfanyl)-3[(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)-one show that higher negative charges are located on the N and O atoms and a higher positive charge is obtained by H. Three carbon atoms (C12, C13, and C14) have a positive charge due to the presence of highly electronegative nitrogen and oxygen atoms. Table 6 showing the enol form has the highest negative charges on the O and N atoms with the highest electronegativity. Thus, the enol form has the highest potential to act as a bidentate ligand.
ESP maps are described by the charged regions in the molecule. The different colours represent different values of the electrostatic potential. The potential grows in the following order: red, orange, yellow, green, and  www.nature.com/scientificreports/ blue. The red colour in ESP maps represents the most negative electrostatic potential, while the blue colour reflects the most positive electrostatic potential regions. The ESP surfaces of investigated structures obtained using B3LYP/6-31G(d,p) are shown in Fig. 4. In the enol and keto forms, the ESP show the localization of a significant negative charge on the O atom, while the blue colour appears around the H7 and H8 atoms of the phenylhydrazinylidene ring. Therefore, the O atom has the highest electron donation ability toward metal ions. A significant blue colour on the H attached to O atoms in rotamers has been observed, and the red colour that exists in the region between the N and O atoms is due to the decline of H-bonds. Acidity and basicity. Investigation of our compound shows it has two protons that are attached to either a nitrogen or oxygen atom. The acidity and basicity of any molecule are required to explain its structure, reactivity, and different chemical properties. Furthermore, learning the acidity constants (pK a ) is important for estimating the equilibrium constant (K) of different reactions, specifically those involving proton transfers. When determining the pK a experimentally is difficult, Scheme 2 shows how the thermodynamic free energies cycle can be used to approximate computational methods. The protonated (cation) and deprotonated (anion) structures of the 4-(methylsulfanyl)-3[(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)-one are depicted in Fig. 5. AH, is usually neutral, denoted AH + 2 , typically has a net charge of + 1, for the protonated form, while the corresponding enol/rotamer or keto. The hydroxyl group of the phenylhydrazinylidene ring has been rotated to give the rotamer structure, according to the optimized structure of the deprotonated form. Therefore, the energy of ) and dual-descriptor (Δf k ) evaluated from Natural Population Analysis for Enol, Keto and Rotamer forms at B3LYP/6-31G(d,p). a Atom numbering is given in Fig. 1.

Enol
Keto Rotamer www.nature.com/scientificreports/ the rotamer will be studied throughout the acidity constant calculation from the protonated form. The deprotonated form denoted A − , typically has a net charge of − 1. The equations used for calculating pK a values are given below (Eqs. (13)(14)(15)(16)): where G i (g), ΔG i (solv), and G i (aq) are the standard free energies of the species "i" in the gas phase, the solvation free energy of "i", and the free energy change in aqueous phase, respectively. The G H + g and �G H + (solv) terms are − 6.28 kcal/mol 69,70 and − 265.90 kcal/mol 71,72 , respectively.
To study the strength of the OH and NH bonds, Tables 5 and 6 presented different charges on the N and O atoms for enol, keto, and enol-rotamer structures. Table 7 collects the calculated acidity constant (pK a ) for the protonated and deprotonated structures in ethanol at B3LYP and M06-2X levels. From the obtained results, the values show that the correlation between the computational and experimental acidity constants indicates that the B3LYP/6-311++G(2d,2p) level gives the nearest pK a value to the experimental values.
The experimental pK a of 4-(methylsulfanyl)-3[(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)one was 12.7 17 , and the protonation structure estimated pK a is 17.48, 12.52, and 9.32 at B3LYP/6-31G (d, p), B3LYP/6-311++G (2d, 2p), M06 By comparing the pK a obtained by deprotonation, the enol form is less acidic than its keto and rotamer structures. This can be credited to some parameters such as the presence or absence of hydrogen bonds, the strength of the OH and NH bonds, and the stability of the resulting conjugate base upon deprotonation.
(13) pK a = �G AH + 2 aq /2.303RT Table 6. NBO charges of all atoms a of the investigated systems calculated at the B3LYP/6-31G(d,p) level of theory in the gas phase. a Atom numbering is given in Fig. 1. www.nature.com/scientificreports/ In the gas phase, the intrinsic basicity can be calculated from the proton affinity (PA), which is the negative of the protonation reaction of AH.  The presence of HBs in chemical compounds can contribute to their chemical stability 73,74 and is considered a strong reason for the strength, shifting, and broadening of the absorption peaks. Figure 6 depicts the keto structure with the strongest HB and a large blue shift (until 280 nm), followed by the enol structure (until 300 nm), and finally the lower shift in the rotamer (until 500 nm). The blue shift and hyperchromic effect for keto and enol forms can be returns to the presence of HBs 17 .
As shown in Table 4, the lower Eg of the keto, enol, and rotamer have maximums in the electronic absorption spectra of keto relative to enol and rotamer, which are bathochromically shifted by 17 and 66 nm, respectively. In the UV-Vis spectra, the peaks of keto, enol, and rotamer are extended over 348-438 nm, 272-500 nm, and 280-479 nm, respectively. The strong electronic absorption of keto is assigned to the HOMO −3 to LUMO and HOMO −2 to LUMO +1 transitions. The maximum absorption peak for enol, which appears at a lower wavelength Scheme 2. Thermodynamic cycle of the protonated structures AH 2 + and AH + at different phases (gas (g) and aqueous (s)) for pK a calculation.  To analyze the nature of UV-Vis absorption, Fig. 8 shows the NTOs of keto, enol, rotamar and transition states for the high-intensity excited states at the PBE/6-311+G(d,p) level with solvent effects of acetonitrile through SMD. In Fig. 8, the occupied NTOs are referred to "hole", while the unoccupied NTOs are the "particles" transition orbitals. NTOs can provide a simple description of the excited state rather than the canonical orbitals. For the investigated structures, the dominant transitions are expected to be π − π* and n − π* excitations which makes the analysis of excitations are difficult. However, from Fig. 8, the holes of NTOs can reproduce the bands given in Fig. 6 and Table 8 and the holes are seem to delocalize on the whole molecular structure while the particles NTOs are mainly delocalized on benzene rings which enhances the π-π* excitation.

Conclusions
The density functional methods (DFT) were used to investigate the tautomer and related rotamers of 4 (methylsulfanyl)-3 [(1Z)-1-(2 phenylhydrazinylidene) ethyl] quinoline-2(1H)-one. B3LYP and M06-2× connected with 6-31G (d, p) and 6-311++G (2d, 2p) basis sets have been used for analysis of different structural properties,  www.nature.com/scientificreports/ stability, and aromaticity. The obtained thermo-kinetic results show a relative stability for keto form compared to other forms and high barriers required for enol formation in gas phase and ethanol under the applied temperature range. Using Eckert tunneling correction indicates a great contribution in keto-enol conversion compered to enol-rotomar conversion. Different sites for the nucleophilic and electrophilic reactions were allocated using Fukui functions. UV absorption spectra in ethanol and gas phases were investigated using the time-dependent density functional theory (TD-DFT) methods B3LYP, PBE, PBE0, CAM-B3LYP, M06-2X, b97X-D, and CIS. The TDDFT-PBE/SMD approach shows good harmony with the 1st and 2nd maximum excitation peaks, and the transitions are π-π* transitions. The remarkable chemical shift of a proton at 14.76 and 19.40 ppm in the nuclear magnetic resonance spectrum has been attributed to the existence of low-barrier hydrogen bonds (LBHBs) for the enol and keto forms, respectively. www.nature.com/scientificreports/

Data availability
All data generated through this study are included in this manuscript and the Supporting Information file.